Snell's Law and Conservation of Energy
Assume the follow condition:
A Prism in a vacuum
Now shoot a ray of light through the prism. We know through
observation that the light will slow relative to the refractive
index. However, when the ray of light leaves the prism it speed
back up to 3.0x 10^8 m/s when no additional energy is added to the
system. How can this be?
I know that the conservation of energy must be true, so what am I missing?
The energy of the photon of light does not depend on its
velocity. It does depend on its frequency (red, blue etc). So the
next question you would ask is why is this? But remember a photon
has no "rest" mass, no mass at all if it were not moving, and it has
to be moving.
When we consider light traveling through a prism at the level of individual
atoms, the contradiction goes away. A beam of light is made of a great many
little bundles of light energy called photons. More photons means brighter
light. Higher energy photons means higher frequency light (i.e. a different
When these millions, or perhaps billions, of photons travel through a prism,
photons of light will definitely crash into prism atoms. A photon that hits
an atom is absorbed. If it is a frequency (i.e. color) that the atom can
hold, the light energy stays in the atom, making the atom bounce around.
This is how light heats things up. In most cases, however, the photon does
not stay inside the atom. It is quickly released. The photon travels on
until it hits another atom. All these small delays within the atoms are
what slows down the photons.
Consider two cars being driven at 45 miles per hour through
town. The first car hits
all green lights; there are no delays. The second car hits many red lights;
there are many delays. Both cars move at the same speed (45mph), but the
delayed car travels more slowly.
Dr. Ken Mellendorf
Illinois Central College
If photons were massive, we would indeed have a big problem here!
However, they are massless and the energy of a single photon is related
only to its frequency. The frequency is unchanged during all the
Energy = (Plancks constant) * (frequency)
It is also possible to re-write the energy (or frequency) in terms of
the velocity and wavelength of the light. The velocity changes during
the transitions, going from fast to slow and back to fast as the photons
leave the substance. However, the wavelength of the light also changes
by the same factor during the transitions going from long to short and
back to long.
E = (Planck's constant) * (Velocity) / (wavelength)
= (Planck's Constant) * (Velocity/Index of Refraction) /
(Wavelength/Index of Refraction)
The Index of Refraction cancels itself out and you are left with the same
before and after any transition. All in all, the energy remains constant.
Michael S. Pierce
Materials Science Division
Argonne National Laboratory
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Update: June 2012